A) \[{{(a+b)}^{2}}\]
B) \[{{a}^{3}}+{{b}^{3}}\]
C) \[{{a}^{3}}-{{b}^{3}}\]
D) \[{{(a+b)}^{3}}-3ab(a+b)\]
Correct Answer: B
Solution :
We have, \[x=a+b,\] \[y=a\omega +b{{\omega }^{2}}\] and \[z=a{{\omega }^{2}}+b\omega \] Then, \[xyz=(a+b)(a\omega +b{{\omega }^{2}})(a{{\omega }^{2}}+b\omega )\] \[=(a+b)({{a}^{2}}{{\omega }^{3}}+ab{{\omega }^{2}}+ab{{\omega }^{4}}+{{b}^{2}}{{\omega }^{2}})\] \[=(a+b)({{a}^{2}}+ab{{\omega }^{2}}+ab\omega +{{b}^{2}})\]\[(\because \,{{\omega }^{3}}=1)\] \[=(a+b)[{{a}^{2}}+{{b}^{2}}+ab(\omega +{{\omega }^{2}})]\] \[=(a+b)({{a}^{2}}+{{b}^{2}}-ab)\]\[(\because \,\omega +{{\omega }^{2}}=-1)\] \[={{a}^{3}}+{{b}^{3}}\]
You need to login to perform this action.
You will be redirected in
3 sec
